Parametric amplifier



June 10, 1969 G. WADE 3,449,678

PARAMETRIC AMPLIFIER Original Filed July 10, 1958 Sheet of s ELECTRON MODUL ATI ON EXPANDER APPA/PE/VT MOT/0N 0F ORB/7' CENTER DRIVING O DRIVING o SIGNAL )as E SIGNAL GENERATOR! 1b GENERATOR,

June 10, 1969 G. WADE PARAMETRIC AMPLIFIER Sheet 2 of5 l/VVE/VTOR Glen [Fade ATTORNEY June 10, 1969 G. WADE PARAMETRIC AMPLIFIER ATTORNEY Sheet IIVVEfl/TOI? Glen Mada Original Filed July 10, 1958 United States Patent 3,449,678 PARAMETRIC AMPLIFIER Glen Wade, Wayland, Mass., assignor to Zenith Radio Corporation, Chicago, 111., a corporation of Delaware Continuation of application Ser. No. 747,764, July 10, 1958. This application June 20, 1963, Ser. No. 289,792 Int. Cl. H03f 7/06; Hillj 29/96, 23/16 US. Cl. 330-4.7 26 Claims ABSTRACT OF THE DISCLOSURE An electron beam modulated with signal energy passes through a region in which a field establishes electron resonance for the electrons in the beam. In that region, the electrons are subjected to an inhomogeneous periodically-varying field of quadrupole configuration. In each of the illustrated species, the quadrupole field is created by four electrodes circumferentially spaced around the path of the beam. In one version, wherein a parametric pumping signal applied to the electrodes is twice the frequency of the signal energy carried by the beam, the individual quadrupole electrodes are straight and generally in alinement with the path of the beam. In other versions, wherein the energy from which amplification is obtained may be defined in terms of frequencies either significantly greater or lower than such a twice-frequency relationship, the quadrupole electrodes are skewed or twisted around the beam path or are in the form of individual transmission lines.

This invention relates to parametric amplifiers. More particularly it has to do with the parametric amplification of signal motion present in electron beams. This application is a continuation of copending application Ser. No. 747,764, filed July 10, 1958 by Glen Wade and assigned to the same assignee as the present application.

In the copending application of Robert Adler, Ser. No. 738,546, filed May 28, 1958, entitled Electronic Signal Amplifying Methods and Apparatus, and assigned to the same assignee as the present application, there are disclosed a variety of signal amplifying devices. In general, these devices include an electron source for projecting an electron beam along a predetermined path terminating in a collector for eventually receiving the electron beam. Spaced along the beam path between source and collector are several components including means disposed along a first portion of the path and responsive to applied signal energy for modulating the beam. Next along the path toward the collector are means for expanding the beam modulation after which signal energy is extracted from the expanded beam modulation. The preferred forms disclosed in the Adler application are those which parametrically amplify electron signal motion.

A parametric amplifier is a device in which a reactance which is part of a transmission system is varied periodically by an external energy source. The parametric amplifiers disclosed in the aforesaid application include means responsive to a driving signal and means for establishing an electron resonant frequency for the electrons passing through the expander. A field derived from the driving signal energy has a restoring force component varying in proper phase with respect to the signal motion to impart energy thereto. The present application is directed to improved parametric expanders for amplifying electron signal motion.

It is accordingly a general object of the present invention to provide a new and improved apparatus for parametrically amplifying signal energy appearing on an electron beam.

A more detailed object of the present invention is to provide new and improved parametric amplifying apparatus which achieves a maximum of electron interaction efliciency.

Still another object of the invention is to provide a new and improved parametric amplifier for electron signal motion which is capable of being manufactured with simple techniques and inexpensive parts.

A further object of the present invention is to provide a new and improved parametric electron-signal-motion expander which efiiciently interacts with beam electrons while minimizing the creation of noise in the electron beam.

It is also an object of the present invention to provide a new and improved electron signal motion expander which produces substantially equal expansion in all directions radially of the beam path and maintains the beam centered with respect to the path.

The parametric modulation expander of the present invention is utilized in an amplifying system in which an electron beam modulated with signal energy is projected along a predetermined path. The expander comprises means for creating in the path a field establishing electron resonance for electrons in the beam. In the expander the electrons are in addition subjected to an inhomogeneous periodically varying field which encompasses a substantially field-free region. This field is preferably of a symmetrical quadrupole configuration.

The features of the present invention which are believed to be novel are set forth with particularity in the appended claims. The organization and manner of operation of the invention, together with further objects and advantages thereof, may best be understood by reference to the following description taken in connection with the accompanying drawings, in the several figures of which like reference numerals identify like elements and in which:

FIGURE 1 is a schematic diagram of one embodiment of the present invention;

FIGURE 2 is a diagram of an expander electrode structure together with an illustration of the field configuration thereof;

FIGURES 3 and 4 are diagrams useful in explaining the operation of apparatus constructed in accordance with the present invention;

FIGURE 5 is a diagram of an alternative expander structure and circuitry therefor;

FIGURE 6 is a schematic diagram of apparatus suitable for use in association with expanders constructed in accordance with the present invention;

FIGURE 7 is a perspective view, partially broken away, of an actual embodiment of the present invention;

FIGURE 8 is a cross-sectional view taken along the lines 88 in FIGURE 7;

FIGURES 9, 10 and 11 are cross-sectional views taken respectively along the lines 99, 10-10, and 11-11 in FIGURE 7;

FIGURE 12 is a schematic diagram of alternative apparatus suitable for use in association with expanders constructed in accordance with the present invention; and

FIGURES 13 and 14 are perspective views of additional embodiments of expanders constructed in accordance with the present invention.

In general, an electron-signal-motion parametric expander is associated with means for modulating with signal energy an electron beam projected along a reference path and means for demodulating the amplified signal motion. As illustrated in FIGURE 1, an electron beam is projected along a reference path 50. The electron source for producing the beam may be entirely conventional and preferably includes the usual cathode together with suitable focusing and accelerating electrodes for developing a well defined beam of electrons. A collector may be disposed at the end of the path remote from the electron source and may conventionally include an anode biased at a positive potential.

Disposed in a first portion of beam path 50 is a modulator 53 coupled to a signal source 54. Modulator 53 is an electron coupler capable of imparting energy to the electron beam in response to signal energy received from source 54. While modulator 53 may take various forms it preferably includes means, such as a magnetic or electIostatic field, for establishing an electron resonant frequency for beam-modulation electron motion. A typical such assembly, for transverse electron motion, includes a solenoid surrounding the beam to establish lines of magnetic flux parallel to the beam path and of a strength establishing a selected cyclotron frequency for electron motion. Modulation signals derived from source 54 and having a frequency similar to the cyclotron frequency cause the electrons in the beam to orbit in an expanding helical path. The amplitude of the modulation signal energy in this particular modulator is represented in the beam by the radius of orbital motion as the beam leaves the modulator.

Any of the several known energy transfer mechanisms, including for the case of transverse motion transmission lines and deflection plates spaced alongside the beam, may be utilized to modulate the beam with energy from source 54. As illustrated, modulator 53 includes a pair of deflector plates 56 and 57 located individually on opposite sides of beam path 50. For coupling signal source 54 to modulator 53, a transmission line 58 having one end 59 shorted is coupled at its other end 60 to deflectors 56 and '1. A transmission link 61 is tapped at 69 onto transmission line 58 at a position adjusted to match the impedance of source 54 to that presented by deflectors 56, 57. Transmission line 58 is effectively a quarter wavelength at the frequency h of the signal from source 54; of course, line 58 may be physically longer by additional increments of one-half wavelength.

To establish an electron resonant frequency approximately equal to the signal frequency along the first portion of beam path 50, the space between electrodes 56 and 57 is subjected to a magnetic field of a strength sufficient to establish for electrons in the beam a cyclotron frequency approximately equal to that of the source signal. To this end, deflectors 56 and 57 are placed within a solenoid indicated schematically by arrow H Following input modulator 53 and disposed alongside a second portion of beam path 50 beyond modulator 53 is an electron modulator expander 63. On beyond expander 63 is a demodulator 64 disposed alongside a third portion of beam path 50 and coupled to a suitable load 65. Demodulator 64 may for convenience be identical with modulator 53 although other appropriate electron couplers may be utilized. As illustrated in FIGURE 1, demodulator 64 therefore includes receptor electrodes 66 and 67 which preferably are identical with electrodes 56 and 57. The portion of the electron beam path disposed between electrodes 66 and 67 is likewise subjected to a magnetic field of a strength sufficient to establish for electrons in the beam a cyclotron frequency approximately equal to the frequency of electron signal motion within the demodulator. As in modulator 53, this field may be created by an ordinary solenoid coil encircling electrodes 66 and 67 as indicated by the arrow labeled H In the present instance, it is most convenient to dispose the entire length of the apparatus within a'single solenoid producing a constant homogeneous magnetic field throughout the beam path. However, separate solenoids may be disposed when different field strengths are required as when demodulator 64 is of a type of beam interaction device different from that of modulator 53. Load 65 is coupled to demodulator 64 through a transmission line section 68 in a manner similar to that described above with respect to the coupling between source 54 and modulator 53. Operation of demodulator 64 is the reverse of that of modulator 53. Motion of the electrons in the beam reacts with demodulator 64 to transfer energy from the beam to the demodulator from where it is fed to load 65 by conventional coupling circuitry.

In the present apparatus it is contemplated to remove energy components, at least those corresponding to the modulation mode effected by modulator 53, existing in the beam as it enters the modulator. Such energy components may constitute excess noise which otherwise would be present in the derived output signal. This noise is carried by the electron beam and appears as energy components which are added to the signal components; typical of such electron beam noise is that originating in the electron source. Additional beam component energy may also be present in the form of other signals applied to the electron beam prior to its passage through modulator 53. To the end of removing such signal component energy, modulator 53 is constructed to interact with the fast electron wave. It has heretofore been known that interaction between electron beams and circuits placed alongside such beams can take at least two diiferent forms. Two distinct electron waves can exist in an electron beam at a given frequency as described in more detail in an article entitled Transverse-Field Traveling-Wave Tubes With Periodic Electrostatic Focusing by Robert Adler et al., appearing in the Proceedings of the Institute of Radio Engineers, vol. 44, No. 1, January 1956, at pages 82-89. A simplified interpretation of the electron-wave action may be developed by considering the electron beam as subject to a restoring force derived from the focusing field in transverse-field tubes and the space charge in longitudinal-field tubes. This restoring force enables each electron in the beam to oscillate about its rest position in the beam at a frequency often referred to as the plasma frequency in longitudinal-field tubes and as the previously mentioned cyclotron frequency or transverse-resonant frequency in transverse-field tubes.

Motion of the electrons in he beam at this electronresonant frequency, once excited, persists until disturbed. To excite this motion by means of a helix or equivalent circuit, the velocity of wave propagation on the circuit must be such that the electrons, traveling at a different velocity, see a signal field at their own resonant frequency.

The circuit wave may be either faster or slower than the beam. The phase velocity u of this wave is a function of the velocity M of electron travel, the signal frequency f and the electron resonant frequency L, as follows:

Interaction between electron motions and signal fields leads to diiferent results in the two different cases. For a circuit wave slower than the beam, phase relations are such that in-phase signals on the beam and the circuit tend to augment each other and produce exponential amplification; this is the mechanism conventionally used in traveling-Wave tubes. At the same time, out-of-phase signals on the beam and the circuit tend to suppress each other and produce exponential attenuation.

When the circuit wave is faster than the beam, the phase relationships are such that when the signal on the circuit augments the motion on the electron beam that same motion has the eifect of reducing the signal on the circuit and vice-versa. As a result of this interrelationhip, a signal traveling on the circuit will eventually disappear from the circuit and at the same time appear on the stream. Subsequently the signal will re-appear on the circuit. Conversely, a signal originating on the beam is transferred to the circuit and, further on, is transferred back to the beam. This is a standing-wave phenomenon analogous to the standing waves observed on coupled transmission lines. However, the energy interchange mechanism is not limited to the use of transmission lines. It is known to the art that lumped structures may be arranged to interact with the beam in an equivalent manner.

One interesting aspect of this phenomenon of beamand-circuit signal interchange is the existence of points along the beam where, at a given signal frequency, all of the signal impressed upon the circuit is transferred to the beam as modulation of the specific character of beam interaction employed and all of the energy originally present in the beam as modulation of the same character transferred to the circuit. This interchange of energy between the beam and the circuit is limited to the specific mode of electron motion which constitutes the faster of the two possible electron waves at the particular signal frequency.

By utilizing fast wave interaction, a desired signal may then be transferred to the beam while noise components are extracted therefrom. In addition, induced noise may be minimized; such noise is induced by the beam in conventional electron beam modulator structure and is then once more impressed upon the beam. A system for interacting with an electron beam in this manner to absorb noise is described and claimed in Patent 2,832,001-issued Apr. 22, 1958 to Robert Adler for Electron Discharge systems and assigned to the same assignee as the present invention.

In order then to take advantage of this fast electron wave noise absorption phenomenon, for transverse-mode modulation the interaction elements of modulator 53 have an effective electrical length along beam path 50 such that all fast wave energy components originally in the beam are transferred to the modulator circuit while the energy from signal source 54 is transferred to the beam. As a result, the electron beam leaving input modulator 53 and traveling toward modulation expander 63 contains energy corresponding to the signal energy supplied by source 54 while containing but a minimum, if any, other fast wave energy such as that originally appearing on the beam in the form of noise.

Disregarding for a moment the effect of modulation expander 63, the operation of the modulation and demodulator may then be summarized. In traveling through modulator 53, the electron beam proceeds in a direction parallel to that of the flux lines of the homogeneous magnetic field. The intensity of that field is adjusted to establish a restoring force acting along two orthogonal coordinates on the beam motion so that the cyclotron frequency corresponds to the applied signal frequency. In the present instance wherein transverse signal modulation is utilized, the energy derived from signal source 54 causes each electron in the beam to describe a spiral of increasing radius as it travels through the modulator. It may be noted that in modulator 53 there is no interchange between transverse and longitudinal electron motion. To the signal source, the electron beam in the modulator looks like a pure resistance load; all of the energy given up to the load appears in the form of transverse electron motion.

Modulator 53 interacts efficiently with the fast electron wave but may also react with the slow electron wave on the beam. While lumped electrodes 56 and 57 interact inefficiently with the slow electron wave, such interaction with the slow wave is minimized theoretically to zero by making the effective electrical length of electrodes 56 and 57 equal to an integral multiple of the slow wave-length. With the input modulator properly loaded by a suitable matching resistance, it extracts the fast wave noise signal from the beam; this match is obtained by adjusting the position of taps 69, of transmission link 61 onto line 58, for minimum noise transmission to load 65. When the input loading is precisely adjusted, the fast electron-wave theoretically contains no noise after leaving the input section, except for thermal agitation noise from signal source 54. Thus, deflector electrodes 56 and 57 together with magnetic field H cause the signal energy from source 54 to be interchanged with the energy originally contained in the beam and specifically with the fast-wave noise energy.

Still disregarding the effect of modulation expander 63, the electrons leaving modulator 53 continue on a helical path of constant radius until reaching demodulator 64. With load 65 tapped onto output transmission line 68 and the parameters of that line adjusted so that demodulator 64 sees a pure resistance, the orbiting electrons induce a field across receptors 66 and 67 that forces the electrons to spiral inwardly as they drift through the demodulator. For the present case wherein the modulator and demodulator are identical and both are properly matched to signal source 54 and load 65, respectively, so as to present to the beam the same resistance, electrons leaving demodulator 64 are devoid of signal modulation. The entire energy modulated on to the beam by modulator 53 is extracted from the beam by demodulator 64.

In order to obtain useful gain, the modulation imposed upon the beam in modulator 53 is expanded. That is, expander 63 produces amplification by imparting energy to the electron signal motion. The energy from which gain is derived is supplied by an external source in a form which minimizes the transfer to the beam of noise components present in the external source, at least in the modulation mode to which demodulator 64 preferably is responsive. To this end, the beam electrons are subjected to an electron suspension or restoring-force field within expander 63 and the stiffness of the suspension is periodically varied in phase with electron motion components so as to impart energy to the electron motion. This is achieved by subjecting the electron beam to a time-varying inhomogeneous field during its passage through modulation expander 63. The invention features thus far discussed are described and claimed in the aforesaid application No. 73 8,546.

The time-varying inhomogeneous field as created in accordance with the present invention is of a character such that maximum amplification efficiency is obtainable with minimized side effects which when not eliminated contribute to reduced signal-to-noise ratio. The invention contemplates obtaining such optimized performance by shaping the gain producing field within expander 63 to include an inhomogeneous field surrounding or encompassing as region of small and preferably negligible field intensity as compared with the intensity of the field in all directions outwardly of the encompassed region. Preferably, reference path 50 about which the electrons leaving modulator 53 orbit, and which may therefore be considered as a reference axis for the orbital motion, passes through the center of this negligible-fieldregion, at which point theoretically the field intensity is zero.

While various electrodes arrangements may be employed in the expander for creating a time varying inhomogeneous field having a configuration incorporating the inventive concepts, a theoretically optimum electrode structure is illustrated in FIGURE 2. Four electrodes 70-73 are symmetrically disposed circu-mferentially around reference path 50. Each electrode 70-73 has the shape of an equilateral hyperbola and the electrodes are individually disposed with their intermediate portions facing the beam path and with their terminal portions projecting outwardly therefrom with each terminal portion being spaced generally parallel from the adjacent terminal portion of the next electrode. Oppositely dis posed electrodes 70 and 72 are coupled to one input terminal 75, and the other pair of oppositely disposed electrodes 71 and 73 are coupled to a second terminal 76.

Assuming an instantaneous potential applied across terminals 75 and 76 such that electrodes 70 and 72 are positive while electrodes 71 and 73 are negative, a symmetrical quadrupole field is developed within the space enclosed by the electrodes. The shape of this field is indicated by equi-potential lines 78. The force exerted by the field at any position therein is indicated by force lines 79 which lie perpendicular to the equi-potential lines, the arrowheads on force lines 79 indicating the direction of the force for the polarities applied. To aid in subsequent explanation, orthogonal reference axes are illustrated as passing respectively through the two electrode pairs 70, 72 and 71, 73. The X-axis passing through the positively polarized electrodes is labeled with a minus sign and the Y-axis is correspondingly labeled with a plus sign. The origin of these two axes preferably coincides with a reference path 50 which is disposed at right angles to the plane in which FIGURE 2 is drawn.

As indicated by equi-potential lines 78, the field produced by the electrodes is everywhere inhomogeneous; the field encompasses a region of vanishing intensity. With a perfectly symmetrical quadrupole having its electrodes shaped precisely as equi-lateral hyperbolae, the inhomogeneity is constant and a field-free region is at the exact center where symmetrical cancellation occurs; viewed in transverse section, the field-free region is a point. The field is of uniform strength in a direction parallel to beam path 50, the field-free region being a line which preferably coincides with beam path 50. That is, the field has substantial components at right angles to the path and the intensity and direction of the components are substantially constant along any line parallel to the path; the intensity increases in proportion to the radial distance from the vanishing field region preferably coincident with the path.

In operation, terminals 75 and 76 are coupled to a driving signal source which supplies energy at a frequency i Accordingly, the polarities on the two electrodes pairs 70, 72 and 71, 73 are periodically reversed at the driving signal frequency. The helically orbiting electrons emerging from modulator 53 are projected through the resulting periodically varying field within the expander electrodes.

Electrons passing through expander 63 are also subjected to a homogeneous magnetic field indicated by arrows H and a strength establishing electron resonance for the signal motion being amplified. That is. the strength of the magnetic field is selected so that the cyclotron frequency effectively creates a resonant suspension for the modulated electrons. In the present embodiment, this field is conveniently of the same strength as that of magnetic fields H and H respectively in the modulator and demodulator. Accordingly, the electron resonance fields for the entire device may be derived from a single solenoid encircling all three portions of reference path 50.

When the magnetic field within expander 63 is selected so that the cyclotron frequency equals the signal frequency, the inwardly directed forces derived from the magnetic field act on the orbiting electrons to balance the outwardly directed centrifugal forces of the electron motion so that the initial electron motion acquired in modulator 53 tends to continue through the expander at the same velocity and amplitude existing upon leaving the modulator. The electrons are thus subjected in the expander to a restoring force field tending to maintain the initial electron motion. However, by properly phasing the inhomogeneous field component forces created in the expander, a periodic time varying restoring force field component is added and imparts increased energy to the electron motion.

To understand the mechanism by which additional energy is imparted to the electrons within expander 63, it may be helpful to examine further the characteristics of the field created by electrodes 7073 and the relationship of this field to the electrons orbiting therethrough. For the structure illustrated in FIGURE 2 in which the electrodes are in the shape of equi-lateral hyperbolae, the potential V at any point within the field follows the relation:

where k is a constant and x and y are the distance along the plus and minus axes respectively. As Will be further discussed below, the field near the center of any quadrupole structure is of this general form but between hyperbolic electrodes it is of this form throughout.

The change of field with distance or the inhomogeneity of the field is given by the second partial derivatives of the potential which are independent of location:

Expressed in polar coordinates about the origin of the coordinate axes, the field intensity equals ZkR where R is the radius vector.

With the driving signal applied across terminal and 76 having a frequency twice the signal frequency, the driving signal frequency f will accordingly be twice the rate of periodic electron motion and consequently also twice the cyclotron frequency established by the magnetic field. The alternating field pattern within the quadrupole of the expander may conveniently be represented by two counter-rotating field patterns, each of one-half the amplitude of the actual pattern. Since only a degree rotation of either of these assumed counter-rotating patterns is required to produce phase reversal and degrees rotation (from electrodes 70 to electrode 72 for example) corresponds to one full cycle, the angular velocities of the two counter-rotating patterns are equal to the cyclotron frequency at which the electrons injected in the expander are orbiting. Radius vector R then describes the location of the electron orbit center with reference to the quadrupole center which is chosen as the origin; this is illustrated in FIGURE 3 in which the axes have been separated from the field pattern for clarity of illustration. The signal amplitude is represented by the radius r of the electron orbit.

One of the two counter-rotating patterns revolves in the same sense as do electrons orbiting in the field. From the standpoint of analysis, it is this revolving component which is of interest in the following discussion. The viewpoint adopted is that of an observer at the origin who revolves with the one pattern rotating in the same direction as the electron.

Assume first an electron which orbits about the origin with the radius r so that the radius vector R equals zero. Seen from the revolving frame of reference, this electron stands still. The electron is acted upon only by an apparent DC field of an intensity kr which may be in any direction in the plane of rotation. When the electron is 45 degrees or halfway between the two axes of the revolving pattern, the field is purely tangential and produces a cyclotronlike increase in orbital velocity; the radius r increases proportionately and since the field is proportional to the radius the process of velocity gain is exponential.

Now assume that the electron is orbiting with the same radius r about a point located away from the origin by the radius vector R. As viewed from the revolving frame of reference, the center of the orbit describes a circle (FIGURE 4) of radius R and moves in a direction opposite to that of the revolving frame of reference. If the electron were as rest at the orbit center it would experience a field of intensity kR which, from the revolving frame of reference, also revolves and averages out to zero over one full cycle. However, an electron orbiting about the orbit center with a radius 2' appears from the reference viewpoint as displaced from the orbit center in an unvarying direction by the distance r. This electron still describes a circle of radius R but the center of this circle is shifted from the origin by a distance r in a direction which depends on the phase of the electron orbit position with respect to the rotation of the coordinate system.

Because the field intensity changes linearly from one point to another by an amount independent of location,

it is permissible to add forces linearly. Hence, the total force exerted upon the electron orbiting ofi center from the origin includes the large revolving portion kR, which averages to zero, and the smaller portion kr which is of constant direction. It will be observed that this constant force is the same as the one developed in the case of an electron orbiting about the coordinate center. It follows that the same effect is observed for all electrons in the beam.

Increased energy is imparted to the motion of an electron by field forces acting tangentially upon the electron in the direction of its movement. Maximum gain is obtained when the electron is subjected to a purely tangential forward force. On the other hand, the electron motion is attenuated when the electron is subjected to a tangential backward force. With respect to the entire beam which is composed initially of many electrons having all different phase relationships with respect to the rotat ing field component, as long as a sufiicient number of the individual electrons have a phase relationship with respect to the inhomogeneous field such that they are subjected to a tangential forward force component, a net gain in signal motion energy is realized since both the gain and the attenuation follow exponential laws of respective growth and decay. Moreover, a phase focusing process takes place which tends to cause electrons with an intermediate phase relationship to be accelerated or decelerated into a phase relationship such that they are subjected to forces producing maximum gain.

The phase focusing mechanism may be understood by first considering the situation in which an electron is subjected to a purely radial field as when the electron is located on the minus axis at the instant when electrodes 70, 72 are negative. Such an electron is pushed inward by the field; this radial force adds to the centripetal force exerted by the magnetic field, as a result of which the cyclotron frequency is raised and the electron drifts ahead in phase. This continues until the radial field component becomes zero in which phase relationship with respect to the field the electron is subjected to a maximum gain producing force.

On the other hand, an electron initially on the plus axis is subjected to an outward force enhancing the centrifugal force; the effect on the electron motion is equivalent to weakening the magnetic field and the electron falls behind in phase as a result of which it drifts into a region in which it is also subjected to a tangential forward force.

Thus, an electron phased so as to have its motion subjected to maximum attenuation is in an unstable condition. The rate of phase correcting is a maximum halfway between the two limiting conditions and becomes zero when the gain maximum is reached. It will be observed that the approach to the phase condition for maximum gain is damped rather than oscillatory.

Because of the phase focusing mechanism, it is desired that the effective electrical length of expander 63 correspond to at least several cycles of the electron orbital motion so that even those electrons which initially enter the quadrupole region with a phase corresponding to the maximum loss condition will be shifted in phase so as to be subjected to a tangential forward force imparting to the electrons increased motional energy.

The change with time of the signal vector r may be easily calculated. For the case of a purely tangential field the usual cyclotron relationship obtains. With a purely radial field, the cyclotron frequency is altered in proportion to the ratio of the force it produces on the electron to the centripetal force exerted by the magnetic field. The incremental change of signal vector r is the same regardless of the direction of the field; in one case the vector in magnitude and in the other it is rotated. The signal vector r may be represented as:

where r is the initial orbital radius, e is the number is 2.718 and t represents time. What may be termed the growth constant a is found to be where k is determined from Equation 1, B is the magnetic field strength. Equation 5 may be further generalized to cover attenuation and phase focusing by assuming the constant k to be a vector which is real and positive when the electron is in the maximum gain condition and which is rotated appropriately for other phase conditions.

Referring to FIGURE 4, during the time in which a maximum-gain-phased electron experiences an amplitude increase of e times, a quadrature-phased-electron drifts into phase by one whole radian. Accordingly, in a high gain amplifier, phase focusing should become fairly complete.

Further insight to the mathematical relationships may be had by deriving from Equation 5 an expression for the gain in terms of gain per unit length of longitudinal electron travel. This relationship may be expressed as:

where v,, is the longitudinal beam velocity. For the illustrated quadrupole, k equals one-half the peak voltage V between adjacent electrodes divided by the square of the half-spacing a between opposite electrodes. It will be observed that the spacing between electrodes may be doubled without changing the results by quadrupling the applied voltage since for the illustrated case k=V /2a Thus far, a theoretically ideal electrode configuration has been described. However, it may be shown that the field near the center of any quadrupole is of the general form of FIGURE 2. Accordingly, operation in accordance with the presently disclosed principles may be had with simpler and easier-to-form electrode shapes and at least near perfect results obtained by restricting the electron signal excursions to the central portion of the field region. It is also unnecessary to restrict the number of electrodes in the expander to four. For example, a larger number of electrodes may be utilized and driven in a multi-phase arrangement to produce an inhomogeneous field periodically varying or revolving in proper relationship to the phase of the periodic signal motion so that the electrons are subjected to forward tangential force components. FIGURE 5 is illustrative of a simplified quadrupole configuration utilizing plate-like electrodes -83 disposed circumferentially around beam path 50. Inductors are coupled individually between adjacent ends of each pair of electrodes 8083. Each of inductors 85 is of a value parallel resonant with the capacity presented across the points of connection at the driving signal frequency f The driving signal source is coupled to the quadrupole by means of a transmission line 86 link coupled to one of inductors 85. In order to correlate the DC potential on the expander with respect to the modulator and the demodulator and to permit proper overall focusing on the beam as it travels along the different path portions, a DC source B+ is coupled to the midpoint of another one of inductors '85. As illustrated in FIGURE 6, driving signal generator 87 has its output terminals 88 matched to transmission line 86 by means of a transformer 89. The magnetic cyclotron field H to which the electrons are also subjected in the expander is applied parallel to the axis of the structure illustrated in FIGURE 5.

When the expander of FIGURE 5 is energized with a driving signal of frequency f which is twice the cyclotron frequency established by magnetic field H electrons following a helical orbit representing signal motion at frequency f are subjected to an increase in that motion in the same manner as previously explained with respect to FIGURE 2. The orbital radius r preferably is confined to the central portion of the field space and is centered about reference path 50. In order to enforce operation of the quadrupole in the 1r mode, opposite electrodes 80,

82 and 81, 83 preferably are electrically tied together by leads and 91 respectively. By the 11' mode is meant operation such that opposite electrodes are in equal phase while adjacent ones are in counterphase.

A practical form of a parametric amplifier constructed in accordance with the present invention is illustrated in FIGURES 7-11. The entire assembly is disposed longitudinally within an elongated evacuated envelope through the opposite ends 101 and 102 of which suitable electrical connecting leads project. Disposed near end 102 is an electron gun assembly 103. The electron gun includes a tubular cathode 104 supported by a ceramic water 105 from a metallic annulus 106 through which an end of cathode 104 freely projects and on which end a cap is disposed and exteriorly coated with an electron emissive material 107 which when heated by heater 108 emits electrons outwardly therefrom. Spaced behind cathode 104 is another metallic annulus 110 forming with annulus 106 a cage substantially confining cathode 104 except for the exposed coating 107. Spaced in front of emissive coating 107 is a metallic wafer 10? having an aperture aligned with the axis of cathode 104 and beam path 50 to limit and define the width of an electron beam projecting through the aperture. Next beyond wafer 109 is an accelerator electrode 111 in the form of a metal disc also having an aperture centered on beam path 50 to accept and pass the electron beam. Successively spaced beyond accelerator 111 are first and second focusing electrodes 112 and 113 likewise having respective apertures centered on beam path 50 and serving in operation to properly form the beam so that it emerges from the electron gun assembly traveling in a direction parallel to beam path 50.

Just beyond electron gun 103 is modulator 53 the electrode configuration of which is shown more clearly in FIGURE 9. In modulator 53, deflectors 56 and 57 are formed of individually outwardly facing channel members spaced on opposite sides of the beam path. For ease of matching source 54 to the deflectors, an inductor 115 is coupled across the deflectors and suitable input leads 116 are tapped across the center thereof.

In the next portion of the beam path outwardly from electron gun 103 is expander 63. In this instance, the expander is a quadrupole composed of electrodes 120 which each have a shape approaching an equi-lateral hyperbola but which are actually formed with a flat intermediate portion 12-1 facing beam path 50 and outwardly projecting terminal portions 122 projecting away from the beam path and spaced generally parallel to the "adjacent terminal portion of the next electrode. As in FIGURE 5, each adjacent pair of electrodes are coupled at the output end of terminal portions 122 to respective ones of inductors 123 which individually have values to tune the quadrupole to a frequency equal to twice the cyclotron frequency established by the magnetic field in which the device is placed in operation. A lead 125 is connected to the midpoint of one of inductors 123 to permit the application of a DC potential to the quadrupole. A conductive loop 126 is coiled coaxially around another of inductors 123 for feeding energy from the external signal source to the quadrupole. Straps 127 interconnect opposite ones of electrodes 121 to enforce operation in the 1r mode. On beyond expander 63 is demodulator 64 which as illustrated is identical in construction with modulator 53. Accordingly, receptors 66 and 67 are disposed on opposite sides of the beam path and the load is coupled by means of outgoing leads 130 tapped centrally across a coil 131 coupled in turn across the receptors.

Just beyond demodulator 64 is an apertured electrode 133 with the aperture centered on beam path 50 and which during operation serves as a suppressor electrode. Finally, the electron beam is collected by an anode 134 disposed transversely of beam path 50 beyond the aperture in suppressor 133. The entire assembly is supported within envelope 100 by means of four ceramic rods 136 symmetrically disposed about beam path 50 and extending through all of the various apertured electrodes and through suitable insulating discs 137 in which the modulator, expander and demodulator electrodes are secured at their respective ends. The various different electrodes are separated by suitable ceramic washers as at 138 encircling ceramic rods 136 between the different electrodes; discs 137 are separated by similar ceramic sleeves as at 139. The entire assembly is held tightly together by means of compression springs 140 acting between a collector mounting plate 141 and a washer 142 pinned to ceramic rods 136. Of course, suitable internal leads are brought out from the various electrodes to the terminals projecting through the base presses. While a flat press is shown in end 102, it is preferred to use a round button as in end 101 in order to reduce interlead capacitance.

In a successfully operated amplifier constructed as illustrated in FIGURES 7 to 11, electron gun 103 included a cathode emitting electron at a current density of about 100 ma./cm. perhaps 99% of which was intercepted by current control element 109. The apertured discs successively spaced in front of the cathode were energized at respective potentials of about 9, 150, 15 and 7 volts positive with respect to the cathode. By slightly varying the relative potentials it was possible to obtain a beam having characteristics resembling Brillouin flow.

The deflectors and receptors respectively in the modulator and demodulator were spaced apart 0.030 inch and the intermediate portions 121 of the expander electrodes formed a square 0.080 inch on each side. In order that the expander would act on at least four orbits of signal motion to obtain substantial gain, the length of electrodes 120 was 0.400 inch, the same as length of modulator and demodulator electrodes. The apertures in the support washers 137 had a diameter of 0.100 inch. The entire structure was sealed within an envelope one inch in diameter.

In operation, the input and output couplers were tuned to 560 megacycles by coils 115 and 131 which were of about nine turns each. The effective capacity of these resonators in the modulator and demodulator was found to be less than one mmfd. and their unloaded Q was about 250. Leads 116 and 130 were 300 ohm transmission lines matched to the couplers which presented an impedance of about 8000* ohms at 40 microamps beam current; so loaded, the effective Q was about 20. Coils 123 tuned the quadrupole to 1120 megacycles.

The tube was placed within a homogeneous magnetic field adjustable to permit variation above and below a strength of approximately 200 gauss. It was found in operation that the DC potential applied to the couplers of the modulator and demodulator had no critical influence on performance; it was approximately 6 volts. The DC potential applied to the quadrupole was found to be somewhat more critical and in general was of a value of between 4 and 7 volts. The collector voltage was 200 volts, all voltages discussed being positive with respect to the cathode.

Having described in detail the basic principles and certain detailed structural embodiments, additional general features of parametric expansion, in common with this and the aforesaid application No. 738,546, will be discussed. During operation, a component of electron motion exists at an idler frequency f which is the difference between driving signal frequency f and signal frequency f With the driving signal frequency exactly equal to twice the signal frequency, the difference frequency is equal to the signal frequency. With the restoring force field H in the expander effectively providing a resonant suspension at the signal frequency, electron resonance also occurs for the electron motion component at the difference frequency. With these two frequencies the same, the two motions become indistinguishable.

While it may appear that to obtain useful amplification the driving signal frequency would need to be exactly equal to twice the signal frequency and of correct phase, it has been found that useful amplification is obtained even though there is considerable variation from these requirements. This will be understood by noting that whenever the driving signal frequency ditfers from twice the signal frequency the orbiting electrons will alternately move into and out of a correct phase relationship for the development of a maximum tangential forward force. The orbital radii are alternately subjected to exponential attenuation and amplification in consequence of departure from the condition wherein the driving signal frequency is exactly twice the signal frequency, and the time average of exponential growth and exponential attenuation yields gain over a Wide frequency range, generally of substantially broader range than the response of the particular modulator and demodulator illustrated.

It was mentioned that when the driving frequency approximates twice the cyclotron frequency the cyclotron field provides a resonant suspension at the idler frequency as Well as at the signal frequency. When the driving frequency departs by a suificiently large amount from twice the cyclotron frequency, the electron resonance of the cyclotron field can no longer be relied on to support the idler frequency. Where desired, an external tuned circuit may be utilized to provide resonance for the idler frequency signal energy. Such a coupling network is illustrated in FIGURE 12 and may be inserted between driving signal generator 87 and transmission line 86. With this network inserted, one side of line 86 is coupled to a corresponding side of a transformer 149 in turn coupled to driving signal terminals 88 through an inductor 150 and a small coupling capacitor 151. The other side of line 86 is similarly connected to the other side of transformer 149 through an inductor 152 and a coupling capacitor 153. An inductor 154 is connected between intermediate taps on inductors 150 and 152 while a capacitor 155 is connected between the ends of inductors 150 and 152 remote from line 86. Inductor 154 together with capacitor 155 and the average capacitance presented by the quadrupole constitute a circuit parallel resonant at idler frequency f At the same time, inductors 150 and 152 together with the average capacitance presented by the expander and capacitor 155 form a series resonant circuit at the driving signal frequency f Other beam interaction devices may be utilized within the modulator and demodulator. Changes may be made in the structure based on the relationships between signal frequency, electron resonant frequency, and phase velocity as explained in detail in the above mentioned article. The condition of operation wherein the electron resonant frequency equals the input signal frequency is characterized by infinite phase velocity of the fast wave. However, when the signal frequency is higher than the electron resonant frequency, the fast electron wave is directed forward and travels at a finite velocity faster than the stream. On the other hand, when the electron resonant frequency is higher than the signal frequency, the fast electron wave travels backward. Dumped structures, such as the deflectors and receptors described above with respect to modulator 53 and demodulator 64, apply a signal simultaneously throughout a finite length and accordingly are most suitable for the condition of infinite phase velocity. Transmission line structures on the other hand may be designed in accordance with well understood principles for any finite phase velocity, forward or backward. Energy interchange between signal and noise may be had between the wave on such a transmission line and the fast electron wave as previously described. A transmission line coupler is therefore suitable for use in either the modulator or demodulator under conditions wherein the signal frequency and electron resonant frequency are unequal. Accordingly, a useful combination comprises a modulator and demodulator of the transmission line type to operate with a finite phase velocity together with an expander which includes simple deflector-type electrodes; Such a combination may utilize a uniform homogeneous magnetic field for all three sections to establish a cyclotron frequency with respect to which the driving signal frequency is within its useful range centered about a frequency twice the cyclotron frequency. In this modification, the cyclotron frequency may be either substantially smaller or substantially larger than the signal frequency. The two cases represent utility at high or low frequencies, respectively. Various applications of these principles and others described hereinafter but which are not claimed herein are described and claimed in copending applications Ser. No. 804,249, filed Apr. 6, 1959 by Robert Adler, entitled Parametric Amplifying Systems, Ser. No. 34,961 filed June 9, 1960 by Robert Adler, entitled Resis tive Loading of Electron Beams on Adjacent Circuit Structures, and Ser. No. 119,931 filed June 27, 1961, by Robert Adler, entitled Electron Beam Amplifiers and Apparatus Therefor, all assigned to the same assignee as the present invention.

It is also contemplated to construct the expander to interact at a finite phase velocity so that the optimum driving signal frequency no longer is equal to twice the electron resonant frequency. An embodiment of this modification of the invention is illustrated in FIGURE 13 which depicts an expander structure to be substituted within envelope in place of electrodes In this modified structure, four helical transmission lines are disposed individually in parallel and spaced circumferentially around reference path 50. At their respective opposite ends, transmission lines 1 60 are supported between Washers 137a in turn held between the modulator and demodulator. The driving signal is fed between two opposite pairs of transmission lines 160.

Being arranged in a symmetrical quadrupole, transmission lines 160 produce an inhomogeneous field within the expander of a shape similar but of course not identical to that illustrated in FIGURE 2. Although it is possible to shape the actual inhomogeneous field produced by transmission lines 160 into a pattern closely resembling that of the hyperbolically shaped electrodes, satisfactory performance may be attained without such complexity since the field near the center of any quadrupole approaches the shape defined by Equation 1 and the electron motion may be confined to this central region.

With interaction at finite phase velocities in the expander, illustrated in FIGURE 13, different magnetic fields may be utilized in the modulator, demodulator and expander, enabling the use of different combinations of finite and infinite phase velocity interaction devices in the three sections. In this case, separate solenoids may be employed about each of the three main sections of the device in order to permit the creation of separate fields.

In the embodiment illustrated in FIGURE 13, the optimum driving signal frequency is no longer equal to twice the electron resonant frequency. A different driving signal frequency exists at which the electrons see a driving signal field alternating at twice the electron resonant frequency. The proper frequency to be applied to the finite phase velocity expander is determined by taking into account the Doppler effect caused by the relative motion of the electrons and the wave along the expander so that the number of field reversals encountered by an electron is approximately four during one electron resonance period.

The invention also contemplates other modifications useful Whenever it may be inconvenient or otherwise undesirable to utilize a driving signal frequency exactly twice the cyclotron frequency while it is yet desired to obtain optimum signal modulation expansion. For example, any of the above described expander electrode assemblies including the transmission lines of FIGURE 13, may be skewed in a direction around the beam path. This is illustrated in FIGURE 14 in which the four quadruple electrodes are composed of four elongated strip-like electrodes 165 secured at their opposite ends between insulating wafers 137b so that the assembly may be substituted between modulator 53 and demodulator 64 of a device such as that illustrated in FIGURES 7-11. In this instance, electrodes 165 all are skewed in the same direction so as to appear as if, after their assembly between supports 137b, one of the supports had been rotated about axis 50 relative to the other.

The operation of the device employing the expander of FIGURE 14 is essentially the same as previously described except that the skewing of the electrodes makes it possible to obtain optimum relationships with a driving signal other than twice the cyclotron frequency. The effect of skewing the electrodes is to cause the quadrupole field to effectively gradually rotate as seen by the electrons moving through the expander. The inhomogeneous field 'has components of substantially constant intensity in a direction parallel to the path but the direction in this instance is not constant. In consequence, if the driving signal frequency is to be lower than that which would otherwise obtain with straight electrodes, electrodes 165 are skewed in the direction of orbital movement so as to compensate for the amount by which the drivingsignal-field alternation actually lags the corresponding rate of periodic electron motion. On the other hand, by skewing the expander electrodes in a direction opposite that of the periodic electron motion, the driving signal frequency may be higher than otherwise needed for the development of an apparent periodic field variation at twice the electron resonant frequency. Particular implementation of these principles is described and claimed in copending application Ser. No. 840,336 filed Sept. 16, 1959 by Glen Wade, entitled Modulation Expander For Parametric Amplifiers and assigned to the same assignee as the present application.

With general reference to all of the various modifications of the expander described, when the elimination of noise is of no concern in the operation of the entire device, simple gaps such as lumped deflectors very short in the direction of electron travel may he used for the modulator and demodulator. On the other hand, it is known to discriminate between the slow and fast wave by using pairs of such gaps spaced and phased with respect to the electron motion so that the undesired wave is cancelled. Accordingly, expanders constructed in accordance with the present invention find advantageous use irrespective of the kinds of modulator and demodulator employed. Amplification of electron motion is obtainable with either fast or slow electron wave interaction. The greatest benefit will usually be obtained through the use of fast wave interaction throughout the tube in order to take fullest advantage of the noise elimination possibilities.

It was noted above that the electron resonant frequency corresponds to the transverse resonant frequency in transverse-field devices and to the plasma frequency in longitudinal-field devices; when the electron resonant frequency is established by l3. magnetic field it is specifically termed the cyclotron frequency. In all cases, the field establishing the electron resonant frequency subjects the electrons to a restoring force field. Para-metric amplification is obtained by adding to this field a periodic field component properly phased to amplify the signal motion. Accordingly, structure for developing a field having a configuration in accordance with the inventive concepts may be advantageously utilized in parametric amplifiers of either the longitudinal or transverse field types or in amplifiers utilizing a combination of both types of fields. Moreover, it may be utilized in devices wherein the signal motion of the electrons is reciprocal rather than helical, and in which electron-resonance field is electrostatic instead of magnetic. Structures for producing periodic electrostatic 16 focusing fields are known to the art for establishing electron resonance.

Additional utility rnay be realized by reason of the fact that parametric electron motion amplifiers resemble frequency converters in many respects. The driving signal at frequency f, may be thought of as the local oscillator frequency. In these amplifiers, an input signal at frequency 1 appears in the output not only as its frequency but also at the idler or difference frequency f At the same time, if there is an input signal at the idler frequency f it will also appear in the output at the signal frequency. In fact, there may be no way of determining at the output whether the original input signal was of frequency f or f With the desired signal at frequency f and observing the output signal at that frequency, electron beam noise at the idler frequency f is converted to frequency f and appears in the output at that frequency. Preferably, the driving signal frequency is approximately twice the desired input signal frequency so that the latter and the idler frequency are close together, as a result of which a single fast-wave-interaction device serves to remove noise from the beam at both the desired and the idler frequencies. In other arrangements wherein the driving signal frequency is substantially different from twice the desired signal frequency so that the idler frequency differs substantially from the desired signal frequency, so long as the idler frequency corresponds to fast electron wave modulation on the beam the noise content may be removed therefrom by an appropriate coupler. Such a coupler for the idler frequency may either be completely separate from the input signal modulator or, alternatively, the latter may be equipped with an additional mesh so that the modulator is also resonant at the idler frequency.

Analysis reveals that the idler frequency corresponds to fast-electron-wave modulation whenever the driving signal frequency is above the input signal frequency. When the driving signal frequency is lower than the input signal frequency, the idler frequency corresponds to a slow-electron-wave and noise absorption is not achieved. However, when extremely low noise is unnecessary, the process of parametric amplification finds utility in an amplifier in which the frequency of the signal being amplified is substantially higher than that of the available driving-signal source. For example, a conventional onethousand 'megacycle oscillator in use as a driving-signal source enables parametric amplification of an input signal having a frequency of two-thousand megacycles or even higher.

An interesting aspect of this parametric frequency conversion process is that levels of signal or noise energy are changed in proportion to frequency when converted from idler to signal frequency or vice versa. Thus, when the driving signal frequency is sufficiently high that the idler frequency is substantially higher than the signal frequency, noise at the idler frequency is attenuated sufficiently by the conversion process that it may in some instances be ignored. On the other hand, when the driving frequency is only slightly higher than the signal frequency, the idler frequency noise is effectively amplified in its conversion to the signal frequency. Accordingly, a relatively low frequency signal, in this instance applied to an input coupler designed to interact at the idler frequency, is substantially amplified; this amplification occurs in addition to the parametric amplification of signals at both the idler and signal frequencies.

There have been disclosed several versions of practically obtainable expanders capable of producing and which have produced worthwhile gain. A number of the characteristics of operation and the desirable features obtainable with the expanders of the present invention are in common with the expanders disclosed in the aforementioned Adler application. In addition, the general form of expander disclosed in the present application is capable of improved performance and is believed to in- 17 corporate to a greater or lesser degree in all of its disclosed forms structure capable of being reasonably easily fabricated and operated and yet which produces an inhomogeneous field configuration approaching the optimum in electron motion expansion performance.

While particular embodiments of the present invention have been shown and described, it will be obvious to those skilled in the art that changes and modifications may be made without departing from the invention in its broader aspects. Accordingly, the aim in the appended claims is to cover all such changes and modifications as fall within the true spirit and scope of the invention.

I claim:

1. In an amplifying system in which an electron beam modulated with signal energy is projected along a predetermined path, a parametric modulation expander comprisin means for creating in said path a field establishing electron resonance for electrons in said beam at a predetermined frequency;

and means for subjecting said electrons to an inhomogeneous time-varying quadrupole field the intensity of which varies linearly with distance from said path and the time variation of which has a phase relationship with the signal modulation on said beam to exert forces on said electrons increasing the energy level of said modulation.

2- In an amplifying system in which an electron beam modulated with signal energy is projected along a predetermined path, a parametric modulation expander comprising:

means for creating in said path a field establishing electron resonance for electrons in said beam at a predetermined frequency;

and means for subjecting said electrons to an inhomogeneous time-varying field encompassing a region of vanishing field strength and the intensity of which varies linearly with distance from said path and the time variation of which has a phase relationship with the signal modulation on said beam to exert forces on said electrons increasing the energy level of said modulation.

3. In an amplifying system in which an electron beam modulated with signal energy is projected along a predetermined path, a parametric modulation expander comprising:

means for creating in said path a field establishing electron resonance for electrons in said beam;

and means for subjecting said electrons to an inhomogeneous time-varying field encompassing a region of vanishing strength substantially centered on said beam path and the intensity of which varies linearl with distance from said path and the time variation of which has a phase relationship with the signal modulation on said beam to exert forces on said electrons increasing the energy level of said modulation.

4. In an amplifying system in which an electron beam modulated with signal energy is projected along a predetermined path, a parametric modulation expander comprising:

means for creating in said path a field establishing electron resonance for electrons in said beam at a predetermined frequency;

and means for subjecting said electrons to an inhomogeneous time-varying field the intensity of which varies linearly with distance from said path and the time variation of which has a phase relationship with the signal modulation on said beam to exert forces on said electrons increasing the energy level of said modulation, the field having a region of substantially constant inhomogeneity and encompassing a region of vanishing field strength.

5. In an amplifying system in which a signal-modulated electron beam is projected along a predetermined path, a parametric modulation expander comprising:

means for creating in said path a field establishing a predetermined electron resonance period for electrons in said beam; and means for subjecting said electrons to an inhomogeneous time-varying field the intensity of which varies linearly with distance from said path and the time variation of which has a phase relationship with the signal modulation on said beam to exert forces on said electrons increasing the energy level of said modulation, the field being of a length along said path encompassing greater than four electron resonance periods and encompassing a region of vanishing field strength. 6. In an amplifying system in which a signal-modulated electron beam is projected along a predetermined path, a parametric modulation expander comprising:

means for creating in said path a field establishing electron resonance for electrons in said beam at a predetermined frequency; and means for subjecting said electrons to an inhomogeneous time varying field the intensity of which varies linearly with distance from said path and the time variation of which has a phase relationship with the signal modulation on said beam to exert forces on said electrons increasing the energy level of said modulation, the field having components of an intensity substantially constant along any line parallel to said path but increasing in proportion to the radial distance from a vanishing field region substantially coincident with said path. 7. In an amplifying system in which a signal-modulated electron beam is projected along a predetermined F path, a parametric modulation expander comprising:

means for creating in said path a field establishing electron resonance for electrons in said beam at a predetermined frequency;

and means for subjecting said electrons to an inhomogeneous time-varying field the intensity of which varies linearly with distance from said path and the time variation of which has a phase relationship with the signal modulation on said beam to exert forces on said electrons increasing the energy level of said modulation, the field having substantial components only at right angles to said path and the intensity and direction of said components being substantially constant along any line parallel to said path but said intensity increasing in proportion to the radial distance from a vanishing field region substantially coincident with said path.

8. In an amplifying system in which a signal-modulated electron beam is projected along a predetermined path, a parametric modulation expander comprising:

means for creating in said path a field establishing electron resonance for electrons in said beam at a predetermined frequency; and

means for subjecting said electrons to an inhomogeneous time-varying field the intensity of which varies linearly with distance from said path and the time variation of which has a phase relationship with the signal modulation on said beam to exert forces on said electrons increasing the energy level of said modulation, the cross-section of said field being skewed around said path in a direction therealong. 9. An amplifying system comprising: an electron source for projecting an electron beam along a predetermined path;

a first source of signal energy;

means coupled to said first source and disposed along a first portion of said path for modulating said beam in response to said signal energy;

means for creating in said path a field establishing electron resonance for electrons in said beam;

a second source of signal energy;

means disposed along a second path portion beyond said first portion and responsive to said second source signal energy for creating an inhomogeneous field the intensity of which varies with distance from said path and having a component effectively rotating around said path in phase with the first source signal modulation on said beam to exert forces on said electrons increasing the energy level of the beam modulation;

and means disposed along a third path portion beyond said second portion for extracting signal energy from said beam.

10. An amplifier device comprising:

an electron source for projecting an electron beam along a predetermined path;

an electron coupler disposed along a first path portion and responsive to energy received from a signal source for modulating said beam;

at least four individual electrodes symmetrically spaced circumferentially around a second path portion beyond said first portion;

means for maintaining said electrodes at a common unidirectional potential;

and an electron coupler disposed along a third path portion beyond said second portion and responsive to modulation on said beam for extracting signal energy therefrom.

11. An amplifier device comprising:

an electron source for projecting an electron beam along a predetermined path;

an electron coupler disposed along a first path portion and responsive to energy received from a signal source for modulating said beam;

a plurality of generally hyperbolically-shaped electrodes symmetrically spaced around a second path portion beyond said first portion, each electrode having an intermediate portion facing said path and terminal portion projecting outwardly therefrom;

means for maintaining said electrodes at a common unidirectional potential;

and an electron coupler disposed along a third path portion beyond said second portion and responsive to modulation on said beam for extracting signal energy therefrom.

12. An amplifier device comprising:

an electron source for projecting an electron beam along a predetermined path;

an electron coupler disposed along a first path portion and responsive to energy received from a signal source for modulating said beam;

a plurality of electrodes spaced around a second path portion beyond said first portion, each electrode having an intermediate portion facing said path and terminal portions projecting outwardly therefrom with each terminal portion spaced from a corresponding terminal portion on the next adjacent electrode;

means for maintaining said electrodes at a common unidirectional potential;

and an electron coupler disposed along a third path portion beyond said second portion and responsive to modulation on said beam for extracting signal energy therefrom.

13. An amplifier device comprising:

an electron source for projecting an electron beam along a predetermined path;

an electron coupler disposed along a first path portion and responsive to energy received from a first signal source for modulating said beam;

a plurality of electrode pairs spaced around a second path portion beyond said first portion;

means coupled individually across each adjacent pair of said electrodes for tuning said electrodes to a predetermined frequency;

means coupled across one of said electrode pairs for feeding thereto energy at approximately said predetermined frequency from a second signal source;

and an electron coupler disposed along a third path portion beyond said second portion and responsive to modulation on said beam for extracting signal energy therefrom.

14. An amplifier device comprising:

an electron source for projecting an electron beam along a predetermined path;

an electron coupler disposed along a first path portion and responsive to energy received from a signal source for modulating said beam;

four electrodes circumferentially spaced around a second path portion beyond said first portion;

means electrically coupling together alternate ones of said electrodes for signal-frequency currents;

means electrically coupling said electrodes in common for unidirectional currents;

and an electron coupler disposed along a third path portion beyond said second portion and responsive to modulation on said beam for extracting signal energy therefrom.

15. An amplifier device comprising:

an electron source for projecting an electron beam along a predetermined path;

an electron coupler disposed along a first path portion and responsive to energy received from a signal source for modulating said beam;

at least four electrodes spaced circumferentially around a second path portion beyond said first portion, said electrodes being skewed around said path;

and an electron coupler disposed along a third path portion beyond said second portion and responsive to modulation on said beam for extracting signal energy therefrom.

16. An amplifying system comprising:

an electron source for projecting an electron beam along a predetermined path;

a first source of signal energy;

an electron coupler disposed along a first path portion and responsive to energy received from said signal source for modulating said beam;

a second source of signal energy;

at least four transmission lines, disposed generally parallel to and spaced .circurnferentially around a second path portion beyond said first portion, coupled to said second source for expanding said modulation on said beam;

and an electron coupler disposed along a third path portion beyond said second portion and responsive to modulation on said beam for extracting signal energy therefrom.

17. In an amplifying system in which an electron beam modulated with signal energy is projected along a predetermined path, a parametric modulation expander comprising:

means for creating in said path a field establishing resonance for motion of electrons in said beam at a predetermined frequency;

and means for subjecting said electrons to an inhomogeneous time-varying quadrupole field the potential of which varies quadradically in the direction of increasing electron motion away from said path and the time variation of which has a phase relationship with the signal modulation on said beam to exert forces on said electrons increasing the energy level of said modulation.

18. In an amplifying system in which an electron beam modulated with signal energy is directed along a predetermined path, a parametric modulation expander comprising:

means for creating in said path a field establishing resonance for motion of electrons in said beam at a predetermined frequency;

and means for subjecting said electrons to an inhomogeneous time-varying quadrupole field within which the change of field intensity is constant in the direc- 21 tion of increasing electron motion away from said path and the time variation of which has a phase relationship with the signal modulation on said beam to exert forces on said electrons increasing the energy level of said modulation. 19. An amplifying system comprising: an electron source for projecting an electron beam along a predetermined path;

a first source of signal energy;

means for creating in said path a field establishing electron resonance for electrons in said beam;

means coupled to said first source and disposed along a first portion of said path for transversely modulating said beam and imparting to said electrons orbital motion representative of said signal energy;

a second source of signal energy;

means disposed along a second path portion beyond said first portion and responsive to said second source signal energy for subjecting said electrons to an inhomogeneous time-varying field, the intensity of which varies linearly in a direction transverse to said path and the time variation of which has a phase relationship with said first source signal energy to increase the orbital radii of said electrons representative of the first source signal energy, said last-mentioned means including a quadrupole electrode system for developing said field and defining a generally cylindrical space within which the orbital electron motion is confined;

and means disposed along a third path portion beyond said second portion for extracting signal energy from said beam.

20. In an amplifying system in which an electron beam, the electrons of which exhibit motion representative of an intelligence signal, is projected along a predetermined path, a parametric electron-motion expander comprising:

means for creating in said path a field establishing electron resonance for said electrons;

and means for subjecting said electrons to an inhomogeneous periodic time-variable quadrupole field, the intensity of which varies linearly with distance from said path and the time variation of which has a phase relationship with said motion to increase the velocity thereof.

21. In an amplifying system in which an electron beam modulated with signal energy is projected along a predetermined path, a parametric modulation expander comprising:

means for creating in said path a field establishing cyclotron electron resonance for electrons in said beam at a predetermined frequency, the electrons traversing helical orbits corresponding to said signal energy and to said field;

and means for subjecting said helically orbiting electrons to an inhomogeneous periodically-varying quadrupole field the intensity of which varies linearly with distance from said path and the periodic variation of which has a phase relationship with the signal modulation on said beam to exert forces on said electrons increasing the energy level of said moduation. 22. In an amplifying system in which a signal-modulated electron beam is projected along a predetermined path, a parametric modulation expander comprising:

means for creating in said path a field establishing cyclotron electron resonance for electrons in said beam at a predetermined frequency;

and means for subjecting said electrons to an inhomogeneous periodically-varying field the intensity of which varies linearly with distance from said path and the periodic variation of which has a phase relationship with the signal modulation on said beam to exert forces on said electrons increasing the energy 22 level of said modulation, the cross-section of said field being skewed around said path in a direction therealong. 23. An amplifying system comprising: an electron source for projecting an electron beam along a predetermined path;

means for creating in said path a field establishing electron resonance for electrons in said beam at a predetermined frequency;

an electron coupler disposed along a first path portion in responsive to energy received from a signal source for modulating said beam;

a potential source;

four electrodes coupled to said potential source and spaced circumferentially around a second path portion beyond said first portion, said electrodes being skewed around said path and, in response to application of the potential from said source, subjecting said electrons to an inhomogeneous periodically-varying field the intensity of which varies linearly with distance from said path and the periodic variation of which has a phase relationship with the signal modulation of said beam to exert forces on said electrons increasing the energy level of said modulation, the cross-section of said field being skewed around said path in a direction therealong.

24. In an amplifying system in which an electron beam modulated with signal energy is projected along a predetermined path, a parametric modulation expander comprising:

means for creating in said path a field establishing electron resonance for electrons in said beam at a predetermined frequency, the electrons traversing periodic excursions corresponding to said signal energy and to said field;

and means for subjecting said electrons to an inhomogeneous periodically-varying quadrupole field the intensity of which varies linearly with distance from said path and the periodic variation of which has a phase relationship with the signal modulation on said beam to exert forces on said electrons increasing the energy level of said modulation.

25. Apparatus for parametrically amplifying signal energy which comprises:

means for projecting an electron beam along a predetermined axis;

means for subjecting electrons in said beam to a magnetic field having its flux lines disposed parallel with said axis; means for modulating said electrons with input signal energy to impart motion to said electrons along a helical path of a predetermined pitch related to the strength of said magnetic field and with a radius representing the amplitude of said signal energy;

means including a plurality of electrode elements for subjecting said electrons to non-homogeneous field forces the strength of which varies substantially linearly with distance from said axis and defining a field pattern with a plurality of pairs of space-opposed poles disposed along inter-leaved helicoidal loci which are coaxial of said helical path, the even numbered pairs of said poles being, at a given time, of one polarity and the odd numbered pairs of said poles being, at the same, of the opposite polarity;

and means for extracting amplified signal energy from said electron motion. 26. An electron discharge device comprising:

means for forming and projecting a beam of electrons along a predetermined path with said electrons exhibiting a predetermined translational kinetic energy; means for establishing resonance for movement of said electrons in a direction transverse of said path;

23 24 input means for imparting transverse resonant motion References Cited to said electrons in response to input signal energy; UNITED STATES PATENTS means for subjecting said electrons to spatially periodic 3,265,978 8/1966 Clavier et a1 O 7 inhomogeneous field components which convert a portion of said translational kinetic energy into trans- 3,233,182 2/1966 Adler 3304-7 verse forces with a phase relationship to said trans- 5 ROY LAKE, Primary Examine):

v 0 ant mot'o to am If th l't de 52: 5 1 n y 6 amp DARWIN R. HOSTETTER, Assistant Examiner. an output means for extracting signal energy from the US. Cl. X.R.

amplified transverse resonant motion. 10 315-3; 330-4.6 

